2D flow simulation over a surface
Starting with a landscape.



Place a plane where your water should be.



(It doesn't have to be that big I just made it big for clarity, all you need is the plane to be as big as the water surface.)

In Edit Mode subdivide the plane.



Add a subdivision Surface modifier and a Displace modifier.

In the display modifier select Texture. (A new one will be created if there are none)

Assign the texture to be used as displacement. I used a wood Texture, but it's up to you how you want the water to flow.

Play with the Strength settings to get the right height for the displacement.





To animate the displacement.

Create an Empty and add a couple of keyframes for the motion.



On the displace modifier set the Texture coordinates as Object 
and Assign the Empty as the object.